A Polynomial Approach to Linear Algebra

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Beschreibung

A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra.
This new edition has been updated throughout, in particular new sections have been added on rational interpolation, interpolation using H^{
fty} functions, and tensor products of models.
Review from first edition:
¿¿the approach pursed by the author is of unconventional beauty and the material covered by the book is unique.¿ (Mathematical Reviews)

Über den Autor

Paul Fuhrmann is a Professor in the Department of Mathematics at Ben-Gurion University of the Negev.

Zusammenfassung

Many additions including Rational interpolation, interpolation using H^{
fty} functions and tensor products and models (scalar case)

Almost 100 new pages added

Allows the reader to access ideas and results on the frontier of current research

Includes supplementary material: [...]

Inhaltsverzeichnis

Preliminaries.- Linear Spaces.- Determinants.- Linear Transformations.- The Shift Operator.- Structure Theory of Linear Transformations.- Inner Product Spaces.- Quadratic Forms.- Stability.- Elements of System Theory.- Hankel Norm Approximation.

Details

Erscheinungsjahr:	2011
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	428
Reihe:	Universitext
Inhalt:	xvi 411 S.
ISBN-13:	9781461403371
ISBN-10:	1461403375
Sprache:	Englisch
Herstellernummer:	80027402
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Fuhrmann, Paul A.
Auflage:	2nd ed. 2012
Hersteller:	Springer US Springer New York Universitext
Maße:	235 x 155 x 24 mm
Von/Mit:	Paul A. Fuhrmann
Erscheinungsdatum:	22.11.2011
Gewicht:	0,645 kg

preigu-id: 107005208